An arithmetic function arising from the Dedekind &psi; function

Defant, Colin
Department of Mathematics, University of Florida

Publication Date

2017-01

Abstract

We define ψ‾ to be the multiplicative arithmetic function that satisfies
for all primes p and positive integers α. Let λ(n) be the number of iterations of the function ψ‾ needed for n to reach 2. It follows from a theorem due to White that λ is additive. Following Shapiro's work on the iterated φ function, we determine bounds for λ. We also use the function λ to partition the set of positive integers into three sets S1, S2, S3 and determine some properties of these sets.